Behaviour of solutions of a singular diffusion equation near the extinction time Original Research Article

We prove that if γ>2 and 0⩽u0∈L1(R2)∩Lp(R2) for some constant p>1 is a radially symmetric function, u0≢0, and u is the unique solution of the equation View the MathML source, in View the MathML source in R2, which satisfies View the MathML source and rur(x,t)/u(x,t)→−γ uniformly on [a,b] as r=|x|→∞ for any 00,β>−1/2,α=2β+1, such that the rescaled function v(y,s)=u(y/(T−t)β,t)/(T−t)α with s=−log(T−t) will converge uniformly on every compact subset of R2 to the solution φλ,β(|y|) of the ODE (rφ′/φ)′/r+αφ+βrφ′=0 in [0,∞] with View the MathML source for some constant λ>0 as s→∞.